mean_ = 1.0;
sigma_hi = 1.0;
sigma_lo = 0.3;

x = linspace(0,5.0,1001);
s = zeros(size(x));

for iii = 1:size(x,2)
   if (x(iii) > mean_)
        sigma = abs(sigma_hi);
    elseif (x(iii) < mean_)
        sigma = abs(sigma_lo);
   else
      sigma = inf; 
   end

    z = (x(iii) - mean_) / sigma;
    s(iii) = exp(-(z^2.0)/2.0); 
end

figure(1)
plot(x, s);
hold on;
plot([mean_ mean_], [0 1.0], '--r');
xlabel('original score');
ylabel('normalized score');